One vs multiple output neurons
This depends on whether the output is a continuous or discrete variable. If the output variable is discrete (there are a finite number of possibilities that it can be), as in a classification task (such as this one, where you are trying to place the input into one of 5 categories), you want to use one output neuron for each class. If the variable is continuous, however, you should only use one output neuron. 

This is because of how the training process works. When training your network successively makes adjustments to try and reduce the errors. These adjustments are made in the direction of the error – so if the network predicts a value which is too high then the network's weights are adjusted to make the output value lower. On the other hand if the network's predicts a value which is too low the network's weights are adjusted to make the output bigger.

If you have output neurons labeled 0 to 4 and a training sample with some input value and a target prediction of 2 then the neural network will make its prediction. Once the prediction has made each neuron is adjusted individually – in this case neuron 2 will be adjusted in the direction of the correct probability and all the other neurons will be adjusted in the direction of the incorrect probability. In this way you have one prediction for each class. 

Backpropagation is a about error attribution, and using multiple neurons allows the error of the neural network to be better attributed as the neural network can adjust each neuron individually, and thus adjust the required probabilities for each class. 

Using a single neuron with a sigmoid activation function would be less good as the sigmoid function saturates values close to 0 and 1 so there would be an unnatural bias towards category 0 and category 4 over the other categories. The neural network could learn to overcome this, but it would take more time.